But is it, I wonder? The planet [sic] is not round...it approximates a human construct called a sphere, but does a sphere exist in nature? Certainly there are good approximations, but an exact sphere is a mathematical construct. The same would apply to other geometrical figures.
"A plant forms in space and is round, that is math. A circle or sphere is the path of least resistance or most efficient use of space. That is math."The question I ask is whether the perception is of 17 buffalo or not. Once we learn symbology then we assign categories, but is that something we do 'inately'? Quantitive awareness depends to some extent on categorisation. We have to agree that A,B and C are of type X before we can go on to ask how many of type X we have.....
I'd like to see why you think Math ISN'T present in us in its most fundamental form before we're taught it. Do you have any evidence of why a baby might prefer two spoons of fudge rather than one? Do you have an explanation as to how we get scared of crowds as children, but are fine with single people? Quantitative awareness, if you would permit, is the root of all math. Understanding that things around us are in numbers, and some numbers are larger than others, while others are of equal magnitude, is how Math came about. I have yet to see proof in this topic about any occurrence in recorded history where any human civilization dating before public education was a norm, was NOT aware of numbers, inequalities, and so on. I can only speak from what I know, which happens to be remarkably small, so maybe I'm wrong. Maybe there WAS a race out there that didn't care if they are 1 buffalo or 17.
posted in errornice try with the eyes' date=' ears, legs, hands, tongues, etc to try and prove a point. you are forgetting one thing though. the less we are born with in the examples you gave, the less likely we WILL survive. plus, we are also getting to the age where people are aborting their fetus if they know the baby will be born handicapped. so you aren't really making a good point here in your examples. in fact, everything you mentioned IS necessary for our survival. sure, technology has helped people more and more with their disabilities as technology grows. even parents and other human being will be a crutch for someone who wont be able to survive on their own with a disability. take away the crutches, and you have a person who wont be able to survive at ALL on their own.[/quote']
If we're going to separate animals from humans because of the advantage an animal has with its animal "instincts" then we have to be equally considerate to the presence of "technology" and "civilization" in human life. In that regard, still, the aforementioned organic assets are not necessary. I would think that you're leaning a bit too deep into Lamarck-ean theory of evolution, where everything that we have now is what we need, and was brought about because the need had, at some point, come into relevance. I agree that a large degree of our current definition of Math is superfluous in the study of "inbuilt Mathematical awareness," but that doesn't mean we can disregard early awareness of inequality, magnitude, and chance, as "too primitive to be Math." I used to term "Logic" earlier here for that same reason. Because we've come so deep into the study of sciences that the concept of counting buffaloes might indeed seem distant from Math. But that is just a difference in our perspectives. I think that awareness of quantity is a sign of Mathematical logic, as opposed to what might otherwise seem to be a barbaric ignorance to the presence of different amounts of different things around us.
yes' date=' the real question at hand is "do we know math before we are taught it". that question also means "do we know math before we are able to teach our own selves math". and this is where it gets tricky. you can't compare an ancient civilization that had the ability to teach itself basic math concepts. you have to imagine a scenario where a baby was born and abandoned on a deserted island where there is no outside influence to learn math. there are many outside influences that could affect that child growing up. [/quote']
So you're saying a baby chick can tell the presence of "addition" and "subtraction" of yellow balls from one pile to the other, and identify which one is of larger quantity just by knowing that "some" were added to it, but a human child could not? You attribute the awareness of this rudimentary degree of logic to Animal Instinct?
I would have to cite my previous assertion that we wouldn't have Math today, if people couldn't understand it from ground zero to begin with. A lot of bricks in a pile don't magically make buildings, a lot of ice doesn't magically make sculptures, so you can't quite say that we have Math today because we "taught" it to ourselves, without admitting that at the very beginning, we could understand it to begin with.
Examples of How Mathematical Logic has been Relevant?
> Hunter Gatherers moved from region to region based off of the total population of animals there, understanding that even though they don't capture "every" animal that they try to, in a place with more animals, their chance of having a steady inflow of meat is greater.
> Early Neanderthals in the France-ish region survived periodic climate changes that their ancestors died from due to the awareness of temperature pattern and readiness to foresee the change in climate before the harsh of winter hit them.
> Mesopotamia relied on a token system to represent value.
It's a difficult thing to do, to analyze what role an abstract entity like the "awareness" of Mathematics plays in our survival, but I'm willing to believe that without the "ability" to quantify and analyze different categories with different numbers of occurrences, we wouldn't be as far as we are (of course).
@ Bikerman. That wasn't my quote, it was the topic starters.
Perfect mathematical ideas rarely ever occur, like true random, a straight line, or a perfect circle. But I'm not going to get into the adherence to mathematical logic in the universe, because you can open a clock with screw head or a Philip's head. Being able to use one doesn't make it the only way to open the clock... in my opion. [/liberalheresy]
now i will give my own example using the topic starter example that you agree with. suppose there are two piles of stones. one pile had 101 pieces. the other had 100. the person who is concluding which pile is bigger is going to say that they are equal. now this is MY proof that the original example is not math but deductive reasoning.
Being unable to tell the difference between 100 stones and 101 stones proves as much about human mathematics as telling the difference between 1000 drops of water, and 1001. Negligibility and human error are aspects of the physical world, and they don't undermine the mathematics behind it. 101 stones > 100 stones. 1001 drops > 1000 drops. Saying that a human can't tell the difference means the human wasn't given enough preparatory conditions to develop a more accurate answer, and doesn't mean the human himself makes all logical decisions based on deduction rather than awareness of inequality.
But on the same note, let's look at some definitions of "Math"
"mathematics: a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement" -wordnetweb.princeton.edu/perl/webwn
"Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions." -en.wikipedia.org/wiki/MATH
Those are the two top most Google Define definitions of the word. It doesn't help the partition in our definitions much, but I'm going to stick with my stance that fundamental math (which I'm saying we all can recognize) deals with the theory of quantities, inequalities, and so on and so forth.Ah...my fault.
@ Bikerman. That wasn't my quote, it was the topic starters. Perfect mathematical ideas rarely ever occur, like true random, a straight line, or a perfect circle. But I'm not going to get into the adherence to mathematical logic in the universe, because you can open a clock with screw head or a Philip's head. Being able to use one doesn't make it the only way to open the clock... in my opion. [/liberalheresy]
On the general topic of inate maths, we certainly have mathematical abilities from around birth. Being able to touch something involves fairly complex 3-D transformations & being able to catch something involves ballistics calculations.
ok. first of all, you aren't understanding my reasoning why we cannot compare other animals to humans. you gave the example of comparing. all i did was try to reason that we cannot do that in this discussion since it would be irrelevant. yes, they are inferior in some ways, but so are WE inferior in other ways. i hope you understand that concept so i don't have to go and list examples. i am just assuming you understand this point. in no way, however, did i ever state that a baby chick can tell the presense of addition and subtraction. i don't even know how you came to understand that that is what i said.i agree with you that math wouldn't be math if nobody was ever able to understand it from ground zero. but it can be LEARNED from ground zero. although it can be learned from ground zero, it doesn't mean math is built in to us. all it means is that math surrounds us and people are always trying to figure out and define what surrounds us. math is no different.you are still using examples of what could have been taught for decades and centuries over time. you give absolutely NO observation to how that relates to math being built in to all humans from birth. you get so off topic with your examples. just becuase we know things, DOESN'T mean why are born with that knowledge. you use a building that requires bricks. you even used the indians again as an example and buffalo where hunting is a LEARNED experience for humans. yes, hunting sometimes involves numbers, but that doesn't mean we were born with that knowledge. forgive me if i don't quote all your examples.....but they don't even show any evidence that math is built in to humans from birth. i used the example of stones as an exagerated example so let's make it less exagerated. since what you are saying is that math is mostly VISUALLY built in to humans. take one pile of stones that has 500 equal pieces and another pile which has 450 equal pieces. i can pretty much assume that most humans would be able to tell which pile is bigger, but some WONT. would that prove or disprove your theory?Being unable to tell the difference between 100 stones and 101 stones proves as much about human mathematics as telling the difference between 1000 drops of water, and 1001. Negligibility and human error are aspects of the physical world, and they don't undermine the mathematics behind it. 101 stones > 100 stones. 1001 drops > 1000 drops. Saying that a human can't tell the difference means the human wasn't given enough preparatory conditions to develop a more accurate answer, and doesn't mean the human himself makes all logical decisions based on deduction rather than awareness of inequality. 1+1=2! not 1+1=2 SOMETIMES depending on how you look at it. but that is what you are concluding since some people will see things different than other people.ok. i like how you broke in to the definition of math, but you really failed to prove a point that EVERY HUMAN that is not "disabled" in any way is able to calculate fundamental math if there are absolutely NO outside influences.now, let's break this down in to simple terms because i am still failing to see what you yourself consider fundamental math. be carefull because i just might show proof that students that have even studied fundamental math in the second grade have failed their tests. so i am sure your definition has NOTHING to do with addition, subtraction, division, or multiplication...but some other form of fundamental math. i would just like to know what this fundemental math is we are now talking about. also, it can't even be visual math since i gave an example to discredit the visual part. but you are saying that math can have logic to it? i say math does not have any logic to it. math has proofs...even elementary math. the visual part or the logic part is what surounds the actual math. the design we can actually see. i think you are getting confused between the two and combining them both thinking both have to do with math.bikerman- being able to touch something means humans have mathmatical abilites from birth? get real.....It is known that babies have a 'grab' instinct from very early - from the point of birth, if not before - and they will seek to grab and hold a finger or other part of a parent in the very early stages after birth. It is suggested that this is an evolutionary adaptation from our tree-climbing days, and this can be illustrated when the baby perceives a danger of falling - the 'grab' reflex is strong and instant.
bikerman- being able to touch something means humans have mathmatical abilites from birth? get real.....
The implications are quite profound : grabbing a finger placed in the palm is not a particularly taxing problem, but working out when to grab is. Having worked on some vision-control computer systems I know some of the issues and complexities involved. How does the baby know it is in danger of falling? The available data is limited - some feedback from the inner-ear, but not much at so young an age; visual clues, but again pretty limited in very young babies, since they cannot focus properly; feedback from muscles and nerves would be the final input. Already there is some serious processing going on to work out when it is necessary to grab - and this is hours after birth, before the baby has chance to experiment by trial and error.
As the baby develops it learns to grab objects in free-space. This could be reaching out for a toy, reaching for a parent's hand. This involves a whole series of calculations, even if unconscious. There are distances to be factored, as well as movement in space. There are estimates to be made (of reach, distance, speed) and there is often some element of prediction/anticipation required. All this is going on in the brain without the baby being conscious of it. It is certainly maths and, what is more, I would be prepared to bet a substantial amount that you can't even do the maths necessary for a task as simple as catching a ball now, as an adult.
The child does it fairly naturally.
Watch a group of girls doing a skipping or ball game. Watch a juggler. The mathematics is obvious and high level. Differential calculus is the tools that we would use to tackle this sort of problem (involving multiple objects moving at different veolocities and accelerations) but the brain just needs a bit of practice in most cases and away you go.
hmmm....interesting, bikerman.... you are the only one to give minor facts that relate to the topic here. part of your so called facts though is to presume babies have a natural instinct related to past generations and evolution. i wouldn't call it evidence, but it is certainly something to think about....i have to sober up a little before i give my full opinion hereIt is not merely a presumption, it is supported by good evidence. Exactly the same grab response can be observed in tree dwelling/using primates such as chimps, and various monkey species. Interestingly a baby also has the same reflex in the feet, although obviously they are evolved to a point where that is of little practical use.
hmmm....interesting, bikerman.... you are the only one to give minor facts that relate to the topic here. part of your so called facts though is to presume babies have a natural instinct related to past generations and evolution. i wouldn't call it evidence, but it is certainly something to think about....
i have to sober up a little before i give my full opinion here
If you have never tried it then you might be surprised just how strongly a newly born baby will grasp a finger placed in its palm.
The evolutionary origin is also supported by other reflexes/behaviours present in babies. One such is the parachute reflex. If you watch a baby falling forwards it will instinctively throw its arms out wide. This is counter intuitive for land-dwelling species - you would expect the baby to instinctively cover the face/head region. It makes sense for an arboreal species, however, because it increases drag, slows down the rate of descent, and gives the baby a better chance of surviving a fall from height.
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